In the rare-earth magnetic pyrochlore oxides, of chemical formula R2M2O7, the rare-earth ions, R
, sit on a pyrochlore lattice of corner-sharing tetrahedra (M
is a non-magnetic transition metal ion). This lattice structure leads to a large degree of geometric frustration for Heisenberg spins with nearest-neighbor exchange coupling. High degree of frustration often drives exotic physics such as spin liquid behavior and other unusual collective and thermodynamic phenomena. The search for such novel phenomena in the R2M2O7 compounds has been the main motivation behind the worldwide experimental effort devoted to the study of these materials for the past ten years or so. In this talk, I will review some of the paradoxical behaviors displayed by these systems, including spin liquid behavior in the Ising-like Tb2Ti2O7 compound, emergent two-dimensional-like correlations in the XY-like Yb2Ti2O7 material and persistent low-temperature spin dynamics in the Heisenberg Gd2Sn2O7 compound.